Answer:
<h2>-3 ; 3</h2>
Step-by-step explanation:
4x² - 36 = 0 ⇌ (2x)² - 6² = 0 ⇌ (2x - 6)(2x + 6) = 0 ⇌ 2x - 6 = 0 or 2x + 6 = 0
⇌ x = 3 or x = -3
Answer:
-312
Step-by-step explanation:
9514 1404 393
Answer:
96 yards
Step-by-step explanation:
The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.
The diagonal is the hypotenuse, so we have ...
100² = 28² + w²
w = √(10000 -784) = 96
The width of the park is 96 yards.
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<em>Additional comment</em>
The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).
You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.
Answer:
Step-by-step explanation:
The area of a triangle is given by the formula:
● A = (b×h)/2
b is the base and h is the heigth.
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Draw the heigth. This gives you two small right triangles.
Let's focus on the right one containing 45°.
● sin 45° = h/8
● h = sin 45° × 8 = 4√(2)
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Replace h by its value in the area formula. The base is 17
● A = (17× 4√(2))/ 2
● A = 34√(2)
● A = 48.08
Round to the nearest unit
● A = 48
